Space capture actuators face problems such as insufficient flexibility and electrical components that are vulnerable to extreme space environments. To address these problems, a centralized-driven flexible continuous robot based on a multiple scissor mechanism units is proposed in this study. The continuous robot body is composed of two scissor mechanism units coupled in series, and the base container’s three motors to drive the robot. The two scissor mechanism units ensure a wide range of flexible operations and the light weight of the robot. The centralized drive with three motors not only reduces the number of driving sources, but also ensures temperature control and protection of electrical components in the space environment. The kinematics and dynamics of the robot are analyzed, and the workspace and deformation performance of the robot are verified through experiments. Compared with other continuous robots, the proposed continuous robot retains the characteristics of continuous robots in a wide range of flexible operations. At the same time, the configuration is light and a small number of driving sources are used, which is suitable for extreme temperatures, vacuum, radiation, and strict resource-constrained environments in space.